Modeltheoretic Semantics and the Syntax-Semantics Interface
Eddy Ruys and Yoad Winter

Course Description

In this course we will introduce elements of semantic theory and the theory of the syntax-semantic interface. Our main aim is to discuss issues which are necessary for the comprehension of contemporary work in these domains within linguistic research.

The course will be divided into three sections:
Section A: preliminaries of modeltheoretic semantics
Section B: preliminaries of the syntax-semantics interface
Section C: a case study - the scope of indefinites


SECTION A
1. Basic notions of modeltheoretic semantics
We will discuss basic intuitions relevant for semantic theory, like entailment, equivalence, contradiction, and truth in a model. For instance: sentence (1) entails sentence (2) because (1) cannot be true unless (2) is. 
 (1) Mary sang and danced.

 (2) Mary sang.
We will introduce the way in which modeltheoretic semantics accounts for such meaning relations. Then we elaborate on the principle of compositionality: the matching between the structure of an expression and its meaning. We will discuss structural ambiguity and show its relations with the compositionality principle.

2. Types and boolean structure
We will discuss the usefulness of a recursive definition of types for describing the relation between syntax and semantics. The category-to-type matching and its implications for the syntax-semantics interface will be briefly introduced.
Then we elaborate on certain types which are of importance for the treatment of coordination and negation phenomena: the Boolean types. We will discuss the Boolean paradigm on natural language semantics and will compare it the traditional "conjunction/negation reduction" approach.

3. Generalized quantifiers
The uniform meaning of NPs as sets of sets will be introduced. The centrality of monotonicity properties will be shown for entailments like (3)=>(4). 
(3) Every man arrived.

(4) Every tall man arrived.
Other important properties of determiners will be introduced: conservativity, extension and permutation invariance. We then discuss two case studies: negative polarity items and "there" sentences.

4. Interlude: lambdas in semantics
We will go through the basic properties of higher order logics for the representation of natural language semantics. Especially: the lambda calculus.

SECTION B
This part of the course focuses on syntactic rules and generalizations that are specifically held responsible for phenomena at the interface with semantics. The primary focus will be on properties of natural language syntax that determine the scope relations among expressions denoting generalized quantifiers.
As a first approximation we will discuss the syntactic movement rule known as Quantifier Raising (QR). The effects of QR account for certain apparent violations of the principle of compositionality, and also results in ambiguities such as in (5).
(5) A picture of every girl was sitting on his desk.
The syntactic restrictions on QR (islands) will be investigated and its characterization as a rule of syntax justified.
In subsequent sessions we will discuss independent evidence for QR and the associated syntactic representation known as Logical Form (LF). Such evidence may be gleaned from VP ellipsis, antecedent contained deletion and elliptic conjunctions. We will pay particular attention to the semantic analysis of these phenomena.

SECTION C
The closing sessions of the course are dedicated to a case study: the interpretation and scope properties of indefinite noun phrases. Such NPs appear to violate the principle of compositionality without being amenable to treatment in terms of QR. For instance, sentence (6) cannot get the structure in (7) using QR, but it does have a meaning that corresponds to that structure.
(6) If a particular white building in Washington is attacked by terrorists 
    then the US security will be threatened.
(7) [a particular white building in Washington] [if e is attacked by terrorists
    then the US security will be threatened
We will compare several competing approaches and argue in favour of the choice function approach.